Question: Simplify the following expression: $x = \dfrac{25p - 45}{50p + 10}$ You can assume $p \neq 0$.
Find the greatest common factor of the numerator and denominator. The numerator can be factored: $25p - 45 = (5\cdot5 \cdot p) - (3\cdot3\cdot5)$ The denominator can be factored: $50p + 10 = (2\cdot5\cdot5 \cdot p) + (2\cdot5)$ The greatest common factor of all the terms is $5$ Factoring out $5$ gives us: $x = \dfrac{(5)(5p - 9)}{(5)(10p + 2)}$ Dividing both the numerator and denominator by $5$ gives: $x = \dfrac{5p - 9}{10p + 2}$